
So far, we have explained how the feature extractor \(\Phi _{\mathbf {\theta }}\)  is adapted by Spacing Loss. Our complete model extends this backbone with one head for the labeled data \(F_{Lab} = \Phi _{Lab} \circ \Phi _{\mathbf {\theta }}\)  and another for the unlabeled data \(F_{Ulab} =\Phi _{Ulab} \circ \Phi _{\mathbf {\theta }}\) . \(F_{Lab}\)  is learned with the labeled examples. \(F_{Ulab}\)  is learned with pairwise pseudo labels derived from cosine-similarity [1]} between its latent representations. We also enforce consistency in prediction with an augmented view of each image [1]}, [3]}, [4]}, [5]} to enhance learning.
While learning a two-stage model, we first learn \(F_{Lab}\)  using cross entropy loss with labeled data and then learn \(F_{Ulab}\)  with these auxiliary losses and Spacing Loss operating in the latent space. Labeled and unlabeled data, along with all the losses are used to learn the single-stage model. During inference, we do a \(k\) -means [6]} on the latent representations from the backbone network, to discover novel categories.
